CN108885239B

CN108885239B - System and method for real-time parameter estimation of rechargeable batteries

Info

Publication number: CN108885239B
Application number: CN201680082175.9A
Authority: CN
Inventors: 郭庆之; 克里斯汀·库珀
Original assignee: Keraishi Advanced Solutions Co ltd; Johnson Controls Technology Co
Current assignee: Keraishi Advanced Solutions Co ltd; Johnson Controls Technology Co
Priority date: 2016-02-19
Filing date: 2016-08-02
Publication date: 2022-03-25
Anticipated expiration: 2036-08-02
Also published as: EP3417304B1; EP3417304A1; CN108885239A; US10367235B2; US20170244137A1; WO2017142587A1

Abstract

A battery system includes a battery coupled to an electrical system. The battery system also includes a battery control module electrically coupled to the battery. The battery control module monitors at least one monitoring parameter of the battery, and the battery control module recursively calculates at least one calculation parameter of the battery based on the at least one equivalent circuit model, the at least one monitoring parameter, and the kalman filter.

Description

System and method for real-time parameter estimation of rechargeable batteries

Technical Field

The present disclosure relates generally to the field of batteries and battery modules. In particular, the present disclosure relates to estimating real-time parameters of a rechargeable battery.

Background

This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present disclosure that are described below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

A vehicle that uses one or more battery systems to provide all or a portion of its power to the vehicle can be referred to as an xEV, where the term "xEV" is defined herein to include all vehicles that use electricity as all or a portion of their vehicle power, or any variation or combination thereof. For example, xevs include Electric Vehicles (EVs) that use electric power as all motive power. As will be appreciated by those skilled in the art, a Hybrid Electric Vehicle (HEV), also known as an xEV, combines an internal combustion engine propulsion system with a battery-powered electric propulsion system (e.g., a 48 volt (V) or 130V system). The term HEV may include any variation of a hybrid electric vehicle. For example, a full hybrid powertrain system (FHEV) may use one or more electric motors, only an internal combustion engine, or both to provide power and other electrical power to a vehicle. In contrast, a mild hybrid electric system (HMEV) deactivates the internal combustion engine when the vehicle is idling, and uses a battery system to continue powering the air conditioning unit, radio, or other electronics, and to restart the engine when propulsion is required. Mild hybrid systems may also apply a degree of power assist, such as during acceleration, as a supplement to the internal combustion engine. Mild hybrids are typically between 96V to 130V and recover braking energy through a belt or crank integrated starter generator. Furthermore, micro-hybrid electric vehicles (mhevs) also use a "start-stop" system similar to mild hybrids, but the micro-hybrid system of a mHEV may or may not provide power assist to the internal combustion engine and operate at voltages below 60V. For the purposes of this discussion, it should be recognized that a mHEV generally does not technically use the electricity provided directly to the crankshaft or driveline as power for any portion of the vehicle, but the mHEV can still be considered an xEV because it does use electricity to supplement the vehicle power demand when the vehicle is idling (with the internal combustion engine deactivated) and recovers braking energy through an integrated starter-generator. Further, a plug-in electric vehicle (PEV) is any vehicle that can be charged from an external power source (e.g., a wall outlet), and the energy stored in the rechargeable battery pack drives or helps drive the wheels. PEVs are a subclass of EVs, including all-electric or Battery Electric Vehicles (BEVs), plug-in hybrid electric vehicles (PHEVs), and retrofit electric vehicles, both hybrid electric vehicles and conventional internal combustion engine vehicles.

The xevs described above may provide several advantages over more conventional pneumatic vehicles that use only an internal combustion engine and a conventional electrical system (typically a 12V system powered by a lead-acid battery). For example, relative to conventional internal combustion vehicles, xevs may produce fewer undesirable emission products and may exhibit greater fuel efficiency, and in some cases, such xevs may not use gasoline at all, as with certain types of EVs or PEVs.

As technology continues to evolve, there is a need to provide improved status indicators for battery modules of such vehicles. For example, the power used by an xEV may be provided by a rechargeable battery. While the rechargeable battery is operating, it may be difficult to accurately depict the state of charge of the rechargeable battery. The present disclosure relates generally to estimating real-time parameters of a rechargeable battery during operation of the rechargeable battery and/or an xEV.

Disclosure of Invention

The following outlines specific embodiments disclosed herein. It should be understood that these aspects are presented merely to provide the reader with a brief summary of these particular embodiments and that these aspects are not intended to limit the scope of this disclosure. Indeed, the disclosure may encompass a variety of aspects that may not be described below.

The present disclosure relates to a battery system including a battery coupled to an electrical system. The battery system also includes a battery control module electrically coupled to the battery. The battery control module monitors at least one monitored parameter of the battery, and the battery control module recursively calculates at least one calculated parameter of the battery based on the at least one equivalent circuit model, the at least one monitored parameter, and the kalman filter.

The present disclosure also relates to a method of determining real-time parameters of a rechargeable battery coupled to an electrical system. The method includes monitoring, with a battery control module, at least one monitored parameter of the rechargeable battery during operation of the battery via one or more sensors coupled to the rechargeable battery. The method also includes recursively calculating, by the battery control module, at least one real-time parameter of the rechargeable battery based on the at least one equivalent circuit model, the at least one monitored parameter, and the kalman filter.

The present disclosure also relates to an energy storage component for a vehicle. The energy storage component includes a housing, first and second terminals, and a rechargeable battery disposed in the housing. The rechargeable battery is coupled to the first terminal and the second terminal. The energy storage component also includes a battery control module that monitors at least one monitored parameter of the energy storage component. The battery control module also recursively calculates at least one calculation parameter of the energy storage component based on the at least one equivalent circuit model, the at least one monitoring parameter, and the kalman filter.

Drawings

Various aspects of this disclosure may be better understood by reading the following detailed description and by referring to the accompanying drawings in which:

FIG. 1 is a perspective view of a vehicle (xEV) having a battery system that contributes all or part of the vehicle's electrical power, according to one embodiment of the present method;

FIG. 2 is a schematic cross-sectional view of the xEV of FIG. 1 in the form of a Hybrid Electric Vehicle (HEV) in accordance with an embodiment of the present method;

FIG. 3 is a schematic diagram of a battery system of the xEV of FIG. 1, according to one embodiment of the present method;

FIG. 4 is a 1-RC equivalent circuit model of the energy storage component of the xEV of FIG. 1 in accordance with one embodiment of the present method;

FIG. 5 is a graph of a relationship between Open Circuit Voltage (OCV) and state of charge (SOC) of an energy storage component of the xEV of FIG. 1, according to one embodiment of the present method;

FIGS. 6A and 6B are process flow diagrams depicting methods for calculating energy storage component parameters and determining parameter convergence of an energy storage component in accordance with embodiments of the present method;

FIGS. 7A and 7B are ring buffers for storing data calculated using the process flow diagrams of FIGS. 6A and 6B, according to one embodiment of the present method;

FIGS. 8A and 8B are process flow diagrams depicting a method of calculating capacity of an energy storage component using two linear regression models, according to one embodiment of the method;

FIGS. 9A and 9B are process flow diagrams describing a method of calculating a capacity of an energy storage component using two relaxation open circuit voltage measurements and a Coulomb count according to one embodiment of the method;

FIG. 10 is a process flow diagram depicting a method for directional validation of a capacity estimate of an energy storage component in accordance with an embodiment; and

FIG. 11 is a diagram depicting an embodiment of the process flow diagram of FIG. 10, according to an embodiment.

Detailed Description

One or more specific embodiments will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

The battery systems described herein may be used to provide power to various types of electric vehicles (xevs) and other high-voltage energy storage/consumption applications (e.g., grid power storage systems). Such battery systems may include one or more battery modules, each having a plurality of battery cells (e.g., lithium-ion (Li-ion) electrochemical cells) arranged and electrically interconnected to provide a particular voltage and/or current useful for powering one or more components of, for example, an xEV. As another example, the battery module according to the present embodiment may be combined with or provide power to a stationary power system (e.g., a non-automotive system).

Based on the advantages over conventional gas powered vehicles, manufacturers that typically produce conventional gas powered vehicles may wish to use improved vehicle technology (e.g., regenerative braking technology) within their vehicle production lines. Typically, these manufacturers may utilize one of their traditional vehicle platforms as a starting point. Since conventional pneumatic vehicles are designed to use a 12 volt battery system, a 12 volt lithium ion battery can be used to supplement a 12 volt lead acid battery. More specifically, a 12 volt lithium ion battery may be used to more efficiently capture electrical energy generated during regenerative braking and subsequently supply the electrical energy to power the electrical system of the vehicle.

As vehicle technology advances, high voltage electrical equipment may also be included in the electrical system of the vehicle. For example, a lithium ion battery may supply electrical energy to an electric motor in a mild hybrid electric vehicle. Typically, these high voltage electrical devices use voltages greater than 12 volts, for example up to 48 volts. Thus, in some embodiments, a DC-DC converter may be used to boost the output voltage of a 12 volt lithium ion battery to power high voltage devices. Additionally or alternatively, a 48 volt lithium ion battery may be used to supplement a 12 volt lead acid battery. More specifically, a 48 volt lithium ion battery may be used to more efficiently capture electrical energy generated during regenerative braking and subsequently provide the electrical energy to power the high voltage devices.

Thus, the design choice as to whether to use a 12 volt lithium ion battery or a 48 volt lithium ion battery may depend directly on the electrical devices included in a particular vehicle. However, the operating principles of 12 volt lithium ion batteries and 48 volt lithium ion batteries are generally similar, although the voltage characteristics may differ. More specifically, as described above, both may be used to capture electrical energy during regenerative braking and subsequently supply electrical energy to power electrical devices in the vehicle.

Accordingly, to simplify the following discussion, the present techniques will be described in connection with a battery system having a 12 volt lithium ion battery and a 12 volt lead acid battery. However, one of ordinary skill in the art would be able to adapt the present techniques to other battery systems, such as those having 48 volt lithium ion batteries and 12 volt lead acid batteries.

The present disclosure relates to a battery and a battery module. More particularly, the present disclosure relates to estimating real-time parameters of a rechargeable battery. Particular embodiments relate to lithium ion battery cells that may be used in vehicular environments (e.g., hybrid electric vehicles) as well as other energy storage/consumption applications (e.g., energy storage for an electrical grid).

In view of the foregoing, this disclosure describes techniques for estimating real-time parameters of a rechargeable battery. Conventionally, in order to determine a state of charge (SOC) of a rechargeable battery, the rechargeable battery implements a coulomb counting (e.g., current integration) method. However, these methods typically rely on a preset value of the rated capacity of the battery, which varies from time to time as the battery ages. In addition, these methods are sensitive to measurement errors. Thus, the coulomb counting method can reset when the integration time exceeds a time limit. Furthermore, these methods may rely on Open Circuit Voltage (OCV) measurements of rechargeable batteries. Accurate measurement of OCV may require that the rechargeable battery be idle at room temperature for a long period of time. Due to the constant charging and discharging of the rechargeable battery during vehicle operation, waiting for the battery to idle for a long period of time may not result in a real-time measurement of the SOC. Rather, the battery control unit described in the present disclosure may estimate parameters of the rechargeable battery, such as OCV, in real time or near real time using the systems and methods described in detail below, thereby providing a real-time estimate of the SOC of the rechargeable battery.

To assist in this description, FIG. 1 is a perspective view of an embodiment of a vehicle 10 that may utilize a regenerative braking system. Although the following discussion relates to vehicles having regenerative braking systems, the techniques described herein may be applicable to other vehicles that capture/store electrical energy using batteries, which may include electric and pneumatic vehicles.

As noted above, it is desirable that the battery system 12 be largely compatible with conventional vehicle designs. Accordingly, the battery system 12 may be disposed in a location in the vehicle 10 that would otherwise accommodate a conventional battery system. For example, as shown, the vehicle 10 may include a battery system 12 in a location similar to that of a lead-acid battery of a typical internal combustion engine vehicle (e.g., under the hood of the vehicle 10). Further, as will be described in greater detail below, the battery system 12 may be positioned to facilitate managing the temperature of the battery system 12. For example, in some embodiments, positioning the battery system 12 under the hood of the vehicle 10 may enable air ducts to flow air over the battery system 12 and cool the battery system 12.

A more detailed view of the battery system 12 is depicted in fig. 2. As shown, the battery system 12 includes an energy storage component 14 coupled to an ignition system 16, an alternator 18, a vehicle console 20, and optionally an electric motor 22. In general, the energy storage component 14 may capture/store electrical energy generated in the vehicle 10 and output the electrical energy to power electrical devices in the vehicle 10.

In other words, the battery system 12 may provide power to components of the vehicle electrical system, which may include a radiator cooling fan, a climate control system, an electric power steering system, a movable suspension system, an automatic parking system, an electric oil pump, an electric booster/turbocharger, an electric water pump, a heated windshield/defogger, a window lift motor, a vanity light, a tire pressure monitoring system, a sunroof motor controller, an electric seat, an alarm system, an infotainment system, a navigation feature, a lane departure warning system, an electric parking brake, an exterior light, or any combination thereof. Illustratively, in the illustrated embodiment, the energy storage component 14 powers a vehicle console 20, a display 21 within the vehicle, and an ignition system 16, which ignition system 16 may be used to start (e.g., crank) an internal combustion engine 24.

Additionally, the energy storage component 14 may capture electrical energy generated by the alternator 18 and/or the electric motor 22. In some embodiments, the alternator 18 may generate electrical energy when the internal combustion engine 24 is running. Specifically, the alternator 18 may convert mechanical energy generated by the rotation of the internal combustion engine 24 into electrical energy. Additionally or alternatively, when the vehicle 10 includes the electric motor 22, the electric motor 22 may generate electrical energy by converting mechanical energy generated by movement of the vehicle 10 (e.g., wheel rotation) into electrical energy. Thus, in some embodiments, the energy storage component 14 may capture electrical energy generated by the alternator 18 and/or the electric motor 22 during regenerative braking. Accordingly, the alternator 18 and/or the electric motor 22 are collectively referred to herein as a regenerative braking system.

To facilitate the capture and supply of electrical energy, the energy storage component 14 may be electrically coupled to an electric system of the vehicle via a bus 26. For example, the bus 26 may enable the energy storage component 14 to receive electrical energy generated by the alternator 18 and/or the electric motor 22. Additionally, the bus 26 may enable the energy storage component 14 to output electrical energy to the ignition system 16 and/or the vehicle console 20. Thus, when a 12 volt battery system 12 is used, the bus 26 may carry electrical power typically between 8-18 volts.

Additionally, as shown, the energy storage component 14 may include a plurality of battery modules. For example, in the illustrated embodiment, the energy storage component 14 includes a lead-acid (e.g., first) battery module 28, according to the present embodiment, and a lithium-ion (e.g., second) battery module 30, wherein each

battery module

28, 30 includes one or more battery cells. In other embodiments, the energy storage component 14 may include any number of battery modules. In addition, although the first and

second battery modules

28, 30 are shown adjacent to each other, they may be positioned in different areas around the vehicle. For example, the second battery module 30 may be positioned in or around the vehicle 10, while the first battery module 28 may be positioned under the hood of the vehicle 10.

In some embodiments, energy storage component 14 may include multiple battery modules to utilize a variety of different battery chemistries. For example, the first battery module 28 may use a lead-acid battery chemistry and the second battery module 30 may use a lithium-ion battery chemistry. In such embodiments, the performance of the battery system 12 may be improved because lithium-ion battery chemistries typically have higher coulombic efficiencies and/or higher power charge acceptance rates (e.g., higher maximum charge currents or charge voltages) than lead-acid battery chemistries. In this way, the capture, storage, and/or distribution efficiency of the battery system 12 may be improved.

To facilitate controlling the capture and storage of electrical energy, the battery system 12 may additionally include a control module 32. More specifically, the control module 32 may control operation of components in the battery system 12, such as operation of relays (e.g., switches) within the energy storage component 14, the alternator 18, and/or the motor 22. For example, the control module 32 may regulate the amount of electrical energy captured/provided by each battery module 28 or 30 (e.g., derating the battery system 12 and re-derating the battery system 12), perform load balancing between the

battery modules

28 and 30, determine a state of charge of each

battery module

28 or 30, determine a temperature of each

battery module

28 or 30, determine a predicted temperature trajectory of any of the

battery modules

28 and 30, determine a predicted life of any of the

battery modules

28 or 30, determine a fuel economy contribution of any of the

battery modules

28 or 30, control the magnitude of the voltage or current output by the alternator 18 and/or the electric motor 22, and so forth.

Accordingly, the control module (e.g., unit) 32 may include one or more processors 34 and one or more memories 36. More specifically, the one or more processors 34 may include one or more Application Specific Integrated Circuits (ASICs), one or more Field Programmable Gate Arrays (FPGAs), one or more general processors, or any combinations thereof. In general, processor 34 may execute computer readable instructions related to the processes described herein. Additionally, the processor 34 may be a fixed-point processor or a floating-point processor.

Additionally, the one or more memories 36 may include volatile memory, such as Random Access Memory (RAM), and/or non-volatile memory, such as Read Only Memory (ROM), optical disk drives, hard disk drives, or solid state drives. In some embodiments, the control module 32 may include portions of a Vehicle Control Unit (VCU) and/or a separate battery control module. Additionally, as shown, the control module 32 may be separate from the energy storage component 14, for example, as a stand-alone module. In other embodiments, battery management system 36 may be included within energy storage component 14.

In certain embodiments, the control module 32 or processor 34 may receive data from various sensors 38 disposed within and/or about the energy storage component 14. The sensors 38 may include various sensors for measuring current, voltage, temperature, etc. with respect to the

battery module

28 or 30. After receiving the data from the sensors 38, the processor 34 may convert the raw data into parameter estimates for the

battery modules

28 and 30. In this way, processor 34 may present the original date as data that may provide valuable information to an operator of vehicle 10 related to the operation of battery system 12, and may display information related to the operation of battery system 12 on display 21. Display 21 may display various images generated by device 10, such as a GUI for an operating system or image data (including still images and video data). The display 21 may be any suitable type of display, such as a Liquid Crystal Display (LCD), a plasma display, or an Organic Light Emitting Diode (OLED) display. Additionally, display 21 may include a touch sensitive element that may provide input for adjustment parameters of control module 32 or data processed by processor 34.

The energy storage component 14 may have dimensions comparable to those of a typical lead-acid battery to avoid having to make changes to the vehicle 10 design to accommodate the battery system 12. For example, the energy storage component 14 may have similar dimensions as an H6 battery, which may be about 13.9 inches by 6.8 inches by 7.5 inches. As shown, the energy storage component 14 may be included within a single continuous housing. In other embodiments, the energy storage component 14 may include multiple housings coupled together (e.g., a first housing including the first battery 28 and a second housing including the second battery 30). In still other embodiments, as described above, the energy storage component 14 may include a first battery module 28 located under the hood of the vehicle 10, and a second battery module 30 may be located inside the vehicle 10.

More specifically, fig. 3 shows a schematic diagram of the components of the battery system 12. As mentioned above in the discussion of fig. 2, the control module 32 may regulate the amount of electrical energy captured/provided by each battery module 28 or 30 (e.g., derating the battery system 12 and re-derating the battery system 12), perform load balancing between the

battery modules

28 and 30, determine a state of charge of each

battery module

28 or 30, determine a temperature of each

battery module

28 or 30, determine a predicted temperature trajectory of the

battery module

28 or 30, determine a predicted life of the

battery module

28 or 30, determine a fuel economy contribution of the

battery module

28 or 30, control the magnitude of the voltage or current output by the alternator 18 and/or the electric motor 22, and so forth. In particular, the control module 32 may measure a state of charge (SOC) and/or a state of health (SOH) based on battery parameters measured by the sensors 38.

In some embodiments, energy storage component 14 may include a single lithium ion battery or a plurality of lithium ion batteries coupled in series. In addition, other rechargeable battery chemistries are contemplated. The energy storage component 14 may release stored energy to a load 40, which load 40 may include the ignition system 16, the vehicle console 20, the display 21, the motor 22, and any other electrical components of the vehicle 10. When the energy storage component 14 releases stored energy to the load 40, the alternator 18 and/or the electric motor 22 may provide energy to the energy storage component 14 to replenish stored energy previously released to the load 40. The sensor 38 may measure a battery parameter of the energy storage component 14, and the sensor 38 may transmit the measurement to the control module 32. The battery parameters of the energy storage component 14 may include a terminal voltage measurement, a terminal current measurement, and a battery temperature measurement. The control module 32 processes the measured battery parameters, as described in detail below, to estimate the SOC of the energy storage component 14, the two resistances associated with the equivalent circuit model of the energy storage component 14, and the capacitance associated with the equivalent circuit model. As discussed below with respect to fig. 4, the equivalent circuit model may be a 1-RC equivalent circuit model.

Further, it is understood that the systems and methods described herein may be used to alter the chemical composition of the energy storage component 14. For example, the SOC, resistance, and capacitance of energy storage component 14 may represent a single or multiple lithium ion batteries, a single or multiple lead acid batteries, some combination thereof (e.g., lithium ion batteries electrically coupled in parallel with lead acid batteries), or any other single or multiple battery chemistry. Further, in an energy storage component 14 having multiple battery chemistries electrically coupled in parallel, the SOC, resistance, and capacitance may represent the entire energy storage component 14, or the SOC, resistance, and capacitance may be calculated for each of the multiple battery chemistries.

Fig. 4 shows a 1-RC equivalent circuit model 42 of the energy storage component 14. The 1-RC equivalent circuit model 42 correlates battery parameters (e.g., Open Circuit Voltage (OCV)44,

resistances

46 and 48, and capacitance 50) with measured parameters (e.g., terminal voltage 52, terminal current, and battery temperature) measured by the sensor 38. In addition, the 1-RC equivalent circuit model 42 provides a mechanism for estimating OCV in real time during operation of the vehicle 10. The OCV may be measurable using other methods, such as coulomb counting methods, when the battery system 12 is in a resting state for a long period of time. That is, the OCV of the battery system 12 may be measurable after the battery system 12 has been dormant for one or more hours. Thus, by using the 1-RC equivalent circuit model 42, the sleep period is no longer used, and the OCV can be estimated while the battery system 12 is operating under the load 40.

In the 1-RC equivalent circuit model 42, the resistance 46 (i.e., R)₀) Ohmic resistance representing the current path of the energy storage component 14, resistance 48 (e.g., R)₁) Representing the charge transfer resistance, capacitance 50 (e.g., C) of the energy storage component 14₁) Representing the double layer capacitance of the energy storage component 14. The 1-RC equivalent circuit model 42 is considered to be a 1-RC equivalent circuit model attributed to a single resistor-capacitor pair (e.g., resistor 48 and capacitor 50). The use of the 1-RC equivalent circuit model 42 enables the OCV44 to be determined during real-time driving conditions of the vehicle 10. In the 1-RC equivalent circuit model 42, the

resistances

46 and 48 and the capacitance 50 may generally be time-invariant parameters of the energy storage component 14. Alternatively, the OCV44, which may be used to determine the state of charge of the energy storage component 14, may generally be a time-varying parameter of the energy storage component 14. That is, as the energy storage component 14 is charged and discharged over a period of time, the OCV44 will increase and decrease over time.

Accurate estimation of the OCV44, the

resistances

46 and 48, and the capacitance 50 may be beneficial to control the energy storage component 14 for longer battery life and improved fuel efficiency of the hybrid electric vehicle. For example, FIG. 5 shows a graph 54 that provides a relationship between the OCV44 and a state of charge (SOC) of the energy storage component 14. The SOC is shown in percent along the abscissa 56 of the graph 54. Additionally, the OCV44 is shown as a voltage along an ordinate 58 of the graph 54. The curve 60 represents the relationship between the OCV44 and the SOC of the energy storage component 14. For example, curve 60 may be used as a lookup table to provide an accurate SOC representation of energy storage component 14. When determining the OCV44 of the 1-RC equivalent circuit model 42 based on the measured battery parameters, the value of the OCV44 may be matched to a corresponding SOC percentage. The SOC percentage may provide an accurate indication of the remaining battery life of the energy storage component 14 to an operator of the vehicle 10 in real time during operation of the vehicle 10. Further, it can be appreciated that the OCV44 varies with variations in SOC. For example, the OCV44 may not stabilize at a certain voltage as the SOC of the energy storage component 14 increases or decreases.

Returning to the discussion of fig. 4. The 1-RC equivalent circuit model 42 may be initially derived in discrete time to correlate estimates of the OCV44, the

resistances

46 and 48, and the capacitance 50 (i.e., battery parameter estimates) with a measured terminal voltage 52 and a measured current of the energy storage component 14. A kalman filter is used in the correlation to determine the battery parameter estimate from the measured terminal voltage 52 and the measured current. Using the kalman filter, the control module 32 may update the battery parameter estimate in real-time with limited reliance on predefined battery parameters.

For any arbitrary current source I, the voltage 52 (e.g., V) of the energy storage component 14 may be calculated by the duhamel superposition theorem:

where ξ is the imaginary variable of the integral. The first two terms on the right side of equation 1 (i.e., V)_ocAnd IR₀) An ohmic description of the energy storage component 14 is given because the voltage 52 and OCV44 minus the ohmic drop IR₀It is related. Furthermore, the third term on the right side of equation 1 corresponds to the superposition integral through which the stack is passedIntegrating, the effect of the past current on the OCV44 exceeds the first order effect of the change in average SOC characterizing the energy storage component 14. Older current-potential data points are exponentially less affected than the most recent data points due to the exponential weighting function.

Can be at two arbitrary time steps t_k-1And t_kEquation 1 is evaluated to yield:

and

it may be assumed that the battery current and voltage are measured at fixed time intervals, for example:

thus,

equations

2 and 3 may be combined to yield:

if I (ξ) is approximately l_k-1Can be subtracted from equation 5 to yield:

V_k＝aV_k-1+(1-a)V_OU-I_kR₀-I_k-1[(1-a)R_i-aR₀] (6)

wherein

In addition, if pass (l)_k-1+l_k) The step current of/2. approximates I (ξ), then equation 5 may be subtracted to yield:

furthermore, if passing the piecewise linear equation (I)_k-1+(I_k-I_k-1))/((t_k-t_k-1)x(ξ-t_k-t) Approximating I (ξ), equation 5 may be subtracted to yield:

equation 8 can calculate the battery voltage more accurately than equations 6 and 7 due to the continuous nature of I (ξ) for all time intervals, equations 6 and 7 are derived based on discontinuous step currents. For convenience, equation 8 may be rewritten as:

V_k＝θ_i-l_kθ₃-l_k-1θ₂+θ₄V_k-1 (9)

wherein

θ₁＝(1-θ₄)V_OC (10)；

And

in the present embodiment, equation 9 is used as a battery model to simultaneously recursively estimate four parameters, θ, from measured voltage and current data using the kalman filtering method₁-θ₄. Physical parameters, e.g. V_oc(e.g., OCV 44), R₀(e.g., resistor 46), R₁(e.g., resistance 48), C₁(e.g., capacitance 50) and time constant τ R₁C₁Is based onThe following equation is from θ₁-θ₄The method comprises the following steps:

and

standard kalman filtering methods may be implemented using a dual model process. In order to estimate the four parameters theta₁-θ₄Using the standard kalman filtering method, the state transition model can be described as:

Θ(k+1)＝Θ(k)+R(k) (18)

where R (k) is the process noise vector and theta (k) is the state vector, where theta (k) is the process noise vector₁-θ₄Are the four parameters of the state vector. In contrast to equation 18 and other kalman filtering methods, the alternative kalman filtering method described below does not explicitly compute the state transitions. Instead, the state measurement mode can be described using the following equation:

V(k)＝Φ(k)′Θ(k)+W(k) (19)

where W (k) is the measurement noise and Φ (k) is the regression vector described by the equation:

Φ(k)＝[1 -I(k-1) -I(k) V(k-1)]′ (20)

further, by using the alternative kalman filtering method, the kalman gain k (k) for SOC estimation is calculated using the following equation:

thus, the state transition model may be updated as follows:

Θ(k)＝Θ(k-1)+K(k)[y-Φ′Θ(k-1)] (22)

where y is the battery voltage 52 measured at time step k. Further, the covariance matrix p (k) is updated by the following equation:

P(k)＝[I-K(k)Φ(k)′]P(k-1)+R (23)

in the surrogate Kalman filtering method, θ 1 is identified as a fast time-varying parameter, θ₂-θ₄Identified as a slowly time-varying parameter. To achieve this function using the alternative kalman filtering method, the process noise matrix R is defined using the following equation:

where r is a small value (e.g., r may be set to about 0.001) for controlling θ using the random walk concept₁Variability over time. This enables the kalman filter to estimate time-varying parameters of the rechargeable battery without using a state transition model, which is typically related to calculating SOC variations by current integration or coulomb counting. In addition, by setting the three other values on the diagonal of the process noise matrix R (k) to zero, the invariant parameter or the slowly time-varying parameter θ₂-θ₄Typically remain unchanged.

The computation of the covariance matrix p (k) plays a role in improving the numerical efficiency and accuracy of estimating the cell parameters. Due to truncation and rounding errors in the computer, the alternative kalman filtering method may result in a loss of symmetry and normality of p (k), or may result in divergence. Therefore, in the alternative kalman filtering method, a U-D factorization method for calculating p (k) is implemented. The U-D factorization method improves the normality and symmetry of p (k), which can lead to high estimation accuracy and robustness.

Implementing the kalman filter function using the U-D factorization method may include calculating the following equation:

F＝U’Φ，G＝DF’，α₀＝1(25)

in calculating equation 25, for a range of values from j-1 to j-M, the following equation is calculated:

in addition, for a range of values from j-1 to j-i-1, the following equation is calculated:

further, the value of r is added to D (1, 1) by the following equation:

D(1，1)＝D(1，1)+r (28)

the gain is also calculated using the following equation:

K＝b/α (29)

after completing the calculations of equations 25-29, a new estimate is calculated using the following equation:

Θ＝Θ+K(y-Φ’Θ) (30)

turning now to fig. 6A and 6B, a flow chart of a method 70 illustrates a method of determining battery parameters of the energy storage unit 14 using the above-described alternative kalman filtering method. Initially, at block 72, initialization is performed by the control unit 32. During initialization, the parameter θ may be set₁-θ₄Is assigned to the state vector theta. The initial values of the parameters may be arbitrary because the surrogate kalman filtering method uses the starting point to determine the final value of the parameter, and the surrogate kalman filtering method does not need to correlate with the parameter θ₁-θ₄Is close to the starting point. Thus, the state vector may be initialized to [ 0000 ] during initialization]'. In addition, during initialization, U, may be initialized to an unity diagonal matrix (i.e., a matrix with 1 value assigned to diagonal elements), and D may be initialized to a diagonal matrix with a large value (e.g., 1000) assigned to each diagonal element. The control module 32 becomes responsive to new voltage and current measurements from the energy storage component 14 of the sensor 38When available, this initialization may cause the method 70 to begin training the measurement model, which is represented by equation 9 above. Further, initialization may include setting values for relative error tolerance (RTOL) and scaling factors. RTOL can represent smoothness and flatness criteria and the scale factor can be a factor of battery current to avoid overflow math errors that may be encountered on a fixed-point microprocessor.

Subsequently, at block 74, the data counter may be updated as new data from the sensor 38 becomes available at the control module 32. For example, the following equation may represent a data counter:

k＝k+1 (31)

where k is the current data count. Further, at block 76, the data values measured at the current time step and the previous time step are assigned to the regression vector Φ (k). The measured data values may include measured battery voltage and current values.

At block 78, a kalman filter function is performed. The kalman filter function may include equations 25-30 above. At block 80, by performing a Kalman filter function, may be derived from θ₁-θ₄Extracts the values of the battery parameters (e.g., OCV44,

resistors

46 and 48, capacitor 50, and time constant τ). Further, at block 82, the slave θ is used₁-θ₄The SOC of the energy storage component 14 may be determined based on an OCV-to-SOC lookup table stored in the memory 36 of the control module 32. The OCV to SOC lookup table may generally be based on a curve similar to curve 60 shown in fig. 5.

Blocks 84-96 relate to monitoring the convergence of the estimated values of the

resistances

46 and 48. By monitoring the convergence of

resistors

46 and 48, control module 32 may confirm that the estimated values of

resistors

46 and 48 are time-invariant. Thus, at block 84, the mean and variance of the moving sample window of

resistances

46 and 48 with the number of samples L is recursively determined. In particular, the following equations may be used to determine the mean and variance of the resistances 46 and 48:

if k < ═ L, then

Otherwise

Wherein mu_kAnd σ_k ²Is the mean value of the samples and the resistance R evaluated at time step k_jThe variance of (c). As shown in equations 32 and 33, the recursive formula developed for calculating the sample mean and variance does not involve every data copy, only the new data and the oldest data are included in the mean and variance calculations. Thus, the control module 32 effectively calculates equations 32 and 33.

Subsequently, at block 86, the control module 32 calculates a squared ratio of the variance to the mean of each of the

resistances

46 and 48, and the control module 32 determines which of the two

resistances

46 and 48 has the greater ratio. In addition, once it is determined which ratio is greater, the control module 32 compares the greater ratio to the square of the relative error margin (RTOL). This comparison was used as a smoothness and flatness test. Smoothness and flatness tests may be used to determine whether the estimated parameters no longer change over time after a learning period of the system. Therefore, to determine the convergence of the

resistors

46 and 48, the smoothness and flatness test needs to pass N consecutive times. The value of N may be 5 cycles, 10 cycles, 15 cycles, or any other number of cycles that may reliably indicate convergence of

resistors

46 and 48. Further, if a sampling frequency of 1 second is used for method 70, each cycle of the smoothness and flatness test of block 86 may run for a total time period of 0.1 nanoseconds.

Subsequently, at block 88, if the larger ratio is less than the square of RTOL, the loop counter (e.g., iCheck) is updated by adding 1 to the previous loop counter value. Conversely, if the larger ratio is greater than the square of RTOL, the loop counter is reset to zero at block 90 and the method 70 returns to initialization at block 72. If the loop counter is updated at block 88 (i.e., if the larger ratio is less than the square of RTOL), a determination is made at block 92 whether the loop counter exceeds the value of N. If the loop counter does not exceed the value of N, the method returns to initialization at block 72.

However, if the cycle counter has exceeded the value of N, then at block 94, the average of the

convergence resistances

46 and 48 and the temperature value are stored in the memory 36 of the control module 32. By measuring the values of the

resistors

46 and 48 as a function of temperature, the control module 32 may observe how the

resistors

46 and 48 decrease over time. Measuring the decrease in the

resistances

46 and 48 may enable the state of health (SOH) of the energy storage component 14 to be characterized in terms of an ohmic resistance increase of the energy storage component 14. Once the average of the

convergence resistances

46 and 48 and the temperature value are stored, the cycle counter is reset to zero at block 96 and the method 70 returns to initialization at block 72. The method 70 may be repeated until the control module 32 provides an indication to stop operation.

Turning now to fig. 7A and 7B, a recursive calculation sum of the sample mean and variance of the

resistors

46 and 48 with the sample number L (e.g., as implemented by block 84 of fig. 6A) may be stored in a circular buffer 100 with L storage locations 102. For example, for a sample number L of 10, the ring buffer 100 may include 10 storage locations 102, as shown. When calculating new data 104, including the sample mean and variance of the

resistances

46 and 48, the new data 104 may be stored in one of the storage locations 102. In fig. 7A, empty storage locations 102 are filled with new data 104 in chronological order of recording each sample. Alternatively, as shown in FIG. 7B, the new data 104 is stored in the ring buffer 100 in the storage location 102 of the oldest data value in the manner described below (e.g., R_j(k-9)): such that new data 104 is stored within the ring buffer 100 and old data 106 (e.g., R) is removed from the ring buffer 100_j(k-9)). Thus, only L storage locations 102 are available to store the sample mean and variance with the number of samples L, and old data 106 is removed from the ring buffer 100.

There may also be benefits in estimating the capacity of the energy storage component 14 in real time. The capacity of the energy storage component 14 may be referred to as a state of health (SOH) of the energy storage component 14. The SOH of the energy storage component 14 may indicate a change in the rated capacity of the energy storage component. Discussed in detail below are two complementary methods for estimating the capacity of the energy storage component 14. The first method discussed in connection with fig. 8 provides a linear regression of real-time battery current and voltage using a kalman filter and an equivalent circuit battery model. The second method, discussed with respect to fig. 9, involves monitoring two open circuit voltage relaxation events and calculating the SOH from the two open circuit voltage relaxation events. The control module 32 may perform each of two methods to estimate the capacity of the energy storage component.

Turning now to fig. 8A and 8B, a method 120 for calculating the SOH of the energy storage component 14 is shown. The method 120 is based on two linear regression models that are run serially at each time step. Because the method 120 relies on a linear regression model, the method 120 may provide numerical stability for estimating SOH, since the parameters of the linear regression model will converge even when the initial values of the parameters are arbitrarily selected. Arbitrarily selecting initial values for the parameters may provide a unique advantage over Extended Kalman Filter (EKF) models, which typically rely on accurate initial guesses for parameters of rechargeable batteries due to their nonlinearity. Additionally, the method 120 may provide a higher degree of tolerance to measurement noise and data defects than EKF models.

The partial discharge of the energy storage component 14 may be used to determine the SOH (i.e., capacity) of the energy storage component 14 using the following equation:

where Q is the capacity of the energy storage component 14 in ampere hours (Ah), I is the current in amperes, SOC is the current SOC value, and SOC is the current SOC value₀Is the initial SOC value. As described above, when an estimated or known value of the open circuit voltage is available, the SOC may be obtained from a lookup table similar to curve 60 of fig. 5. Equation 34 can also be rewritten as the following equation:

wherein w is equal to 100/Q and

is the accumulated Ah throughput of the energy storage unit 14. Equation 35 may be used as the dominant equation for battery capacity estimation in method 120. SOC₀And w are both time-invariant parameters that can be estimated if the SOC value is known. The SOC value may be estimated using Kalman filtering techniques, as discussed above in the discussion of FIGS. 6A and 6B. Thus, in method 120, two linear regression models are used. That is, blocks 122 through 132 may determine the SOC value of the energy storage component 14, and block 134 through 156 may provide the SOC using the SOC and Ah throughput as inputs and the convergence determination₀And an estimate of w. Therefore, the battery capacity can be easily calculated from the estimated value of w.

At block 122, the method 120 is initialized. During initialization, any initial value can be assigned to θ for the state vector Θ₁-θ₄. The initial values of the parameters may be arbitrary because the surrogate Kalman filtering method uses a starting point to determine the final value of the parameter, but the surrogate Kalman filtering method does not rely on approaching the parameter θ₁-θ₄Is measured at the start of the actual value of (a). Thus, the state vector Θ can be initialized to [ 0000 ] during an initialization event]'. In addition, during initialization, U, may be initialized to an unity diagonal matrix (i.e., a matrix with 1 value assigned to diagonal elements), and D may be initialized to a diagonal matrix with a large value (e.g., 1000) assigned to each diagonal element. This initialization may enable the method 70 to begin training the measurement model, represented by equation 9 above, when new voltage and current measurements from the energy storage component 14 of the sensor 38 become available to the control module 32. Further, initialization may include setting values for relative error tolerance (RTOL) and scaling factors. RTOL may represent smoothness and flatness criteria and the scale factor may be a factor of the battery current to avoid settling on a pointOverflow math errors that may be encountered on a microprocessor. Linear regression models for SOC estimation and methods for SOC₀And the linear regression model of w, perform initialization at block 122.

At block 124, the data counter may be updated as new data from the sensor 38 becomes available at the control module 32. For example, equation 31 may be used as a representation of the current data count. Further, when data is available, the ampere hour throughput can also be updated using the following equation:

q＝q+Δq_k (36)

where q is the ampere-hour throughput. Further, at block 126, the data values measured at the current time step and the previous time step are assigned to the regression vector Φ (k). The measured data values may include measured battery voltage and current values.

At block 128, a kalman filter function is performed. The kalman filter function may include equations 25-30 above. By performing the Kalman filter function, in addition to the

resistors

46 and 48, the capacitor 50, and the time constant τ, may be measured from θ at block 130₁-θ₄The value of OCV44 is extracted. Additionally, at block 132, the slave θ is used₁-θ₄The SOC of the energy storage component 14 may be determined based on an OCV-to-SOC lookup table stored in the memory 36 of the control module 32. The OCV to SOC lookup table may generally be based on a curve similar to curve 60 shown in fig. 5.

Subsequently, at block 134, the control module 32 determines whether the estimated SOC is available as an input to proceed with subsequent capacity estimation of the energy storage component 14. For example, the control module 32 may make the determination based on whether a battery terminal temperature requirement is met (e.g., the temperature of the terminals of the energy storage component is less than about 25 degrees celsius) and whether a minimum SOC learning period has been exceeded (e.g., the time interval between the current measurement and the initial condition is greater than 100 seconds). If either of these conditions is not met, the current and voltage measurements are reset to previous values at block 136 and the method 120 resumes at the data counter update of block 124.

If SOC is available for capacity estimation, at block 138, minimum and maximum SOC values are tracked for calculating a maximum SOC swing. Further, at block 140, the ampere-hour throughput is assigned to a second regression vector. The second regression vector is represented by Φ 1 and represents the following equation:

Φ1(k)＝[1 q/scale1]′ (37)

where q is the amp hour throughput and scale 1 is a scaling factor of the estimated capacity when calculated on a fixed point microprocessor to avoid overflow mathematical errors.

Once the ampere-hour throughput is assigned to the second regression vector, a kalman filter function is performed at block 142. Executing the kalman filter function may update the covariance matrices U1 and D1 and the parameter vector for capacity estimation Θ 1, which is initialized to [ 0000 ]', along with the parameter vector for SOC estimation Θ. Further, the kalman gain k (k) for capacity estimation is represented by the following equation:

and the covariance matrix P1(k) is updated by the following equation:

P1(k)＝[I-K1(k)Φ1(k)′]P1(k-1) (39).

equation 39 does not include the process noise matrix R when compared to equation 23 for SOC estimation, since SOC₀And w are both time-invariant parameters.

Subsequently, at block 144, the estimated capacity Q may be extracted from the parameter vector Θ 1. For example, the estimated capacity value Q may be represented by the following equation:

Q＝-100/θ1₂ (40)

wherein theta 1₂Is the second parameter from the parameter vector Θ 1. After extracting the estimated capacity value Q, the convergence of the capacity estimate may be monitored using

block

146 and 156.

Thus, at block 146, the mean and variance of a moving sample window of the estimated capacity value Q with the number of samples L is recursively determined and stored in a circular buffer similar to the circular buffer 100 described above. After the mean and variance are determined, the square ratio of variance to mean square is compared to the square of RTOL at block 148. This comparison was used as a smoothness and flatness test. Smoothness and flatness tests may be used to determine whether an estimated parameter (e.g., estimated capacity value Q) is no longer changing over time after a learning period of the system. Therefore, in order to judge the convergence of the estimated capacity value Q, the smoothness and flatness tests are passed N consecutive times. The value of N may be 5 cycles, 10 cycles, 15 cycles, or any other number of cycles that may reliably indicate convergence of the estimated capacity value Q. Further, if a sampling frequency of 1 second is used for method 120, each cycle of the smoothness and flatness test of block 148 may run for a total time period of 0.1 nanoseconds.

Subsequently, at block 150, if the ratio is less than the square of RTOL, the loop counter (e.g., iCheck) is updated by adding a 1 to the previous loop counter value. Conversely, if the ratio is greater than the square of RTOL, then the current and voltage measurements are reset to previous values at block 136 and the method 120 resumes at the data counter update of block 124. If the cycle counter is updated at block 150 (i.e., the larger ratio is less than the square of RTOL), then a determination is made at block 152 whether the cycle counter has exceeded the value of N and the SOC swing (maximum SOC minus minimum SOC) is greater than SOC ₀20% of the total. The threshold for the SOC swing at block 152 may also be the SOC₀Depending on the particular energy storage component 14. For example, the percentage may be 25% or up to 50%, or the percentage may be SOC ₀10% or 15%. If the cycle counter does not exceed the value of N and/or the SOC swing is not large enough, the method 120 returns to block 136 to reset the voltage and current values.

If the cycle counter has exceeded the value of N and the SOC swings sufficiently, the extracted estimated capacity value Q is saved to memory 36 at block 154. After the estimated capacity value Q is saved to memory 36, the loop counter is reset to zero and the method 120 returns to block 136. Additionally, the method 120 may repeat as described above until the control module 32 receives an indication to stop estimating the estimated capacity value Q of the energy storage component 14.

Fig. 9A and 9B illustrate a method 160 for calculating the SOH of the energy storage component 14 by monitoring two effective Open Circuit Voltage (OCV) relaxation events and integrating the current over time between the two effective OCV relaxation events. The first of the two effective OCV relaxation events may be measured immediately upon starting the vehicle 10 after a longer sleep period (e.g., after the vehicle has been turned off for more than 2 hours), and the second of the two effective OCV relaxation events may be measured when the energy storage component 14 has relaxed for a longer period of time (e.g., after the vehicle 10 has been turned off and a predetermined amount of time has elapsed). Additionally, the time between two valid OCV relaxation events may be limited to limit the accumulation of current offset errors and improve the accuracy of SOH measurements.

At block 162, the method 160 is initialized. Setting a time counter t for starting the ampere-hour throughput ∑ q during initialization₁And t₂And a binary OCV effectiveness state icov. If the OCV of the energy storage component 14 has fully relaxed at the time the control module 32 wakes up (e.g., when the vehicle 10 is started), the value of iOCV may be set to 1 during initialization. Otherwise, the value of iOCV may be set to 0 during initialization. After parking the vehicle at room temperature for a longer period of time (e.g., greater than one hour), the OCV may fully relax with less than the relaxation current threshold/_relaxNegligible current draw value. One method of confirming whether an OCV has fully relaxed is to monitor the rate of change of the OCV over time, as the OCV may change asymptotically over time. The OCV may change very slowly over time after a longer period of time at room temperature, and the relaxed OCV of method 160 may be represented with sufficient accuracy using such an OCV for method 160.

After initialization, at block 164, the counter is updated as new data from the sensor 38 becomes available at the control module 32. For example, equation 31 may be used as a representation of the current data count. Once the counter is updated, at block 166, data is read from the sensor 38 of the energy storage component 14. The data may include battery current, voltage, and step changes in amp-hour throughput. Thus, as the amp-hour throughput is stepped, at block 168, the accumulated amp-hour throughput is updated using the following equation:

∑q＝∑q+Δq_k (41)

where Σ q represents the cumulative ampere-hour throughput, and Δ q_kRepresenting a step change in amp-hour throughput.

At block 170, the control module 32 determines whether the battery current meets a predetermined relaxation current threshold/_Relax. The absolute value of the battery current can be measured at the current time step and is compared with I_RelaxA comparison is made to complete the determination. If the absolute value of the battery current is greater than I_RelaxThe battery is not sufficiently relaxed. At this point, the time step may be monitored, and the iOCV value may be maintained at 0 or set to 0 at block 172. Accordingly, the method 160 may begin again at the counter update of block 164.

Or, if the absolute value of the battery current is less than I_RelaxThen the ivc validity state may be determined at block 174. That is, if the value of iOCV is 1, the energy storage component 14 has been in the relaxed state for a sufficient amount of time, and the OCV may be set to the current voltage reading V at block 178_k. Alternatively, if the iOCV is 0, then at block 176, a determination is made as to whether a sufficient amount of time has elapsed to allow the energy storage component 14 to sufficiently relax. For example, the amount of time from initialization to the current time step may be related to the relaxation threshold time t_RelaxA comparison is made. As mentioned above, under standard operating conditions, t_RelaxCan be set to 1 hour, 2 hours or longer. However, t_RelaxMay be increased or decreased based on external conditions such as the temperature of the battery. Generally, the higher the temperature of the battery, t_RelaxThe shorter the time may be. If the relaxation threshold time t has not been met_RelaxThen the method 160 returns to the counter update of block 164 to begin the method 160 again.

Or, if the relaxation threshold time t has been met_RelaxThe energy storage component 14 has been in relaxationFor a sufficient amount of time, the OCV may be set to the current voltage reading V at block 178_k. According to the current voltage reading V_kThe determined OCV value, the current SOC may be determined from an OCV versus SOC lookup table similar to curve 60 of fig. 5.

Subsequently, at block 182, it is determined whether the counter value k is greater than the number of samples L. If the counter value k is greater than L, the value of the modulus variable M is updated by adding 1 to the value at block 184. The modulus variable M represents the cumulative number of times the OCV standard has been met. Alternatively, if the counter value k is not greater than the number of samples L, the value of L is set to the counter value k plus 1 at block 186. After updating the values of the modulus variable M and/or the number of samples L, a modulus operation is performed at block 188 to alternately record the current SOC value between two memory storage locations within the memory 36 of the control module 32. Thus, the method 160 will alternately store the current SOC value as SOC at block 190₁And stores the current SOC value as SOC at block 192₂. Additionally, the time and cumulative amp-hour throughput may also be stored in memory at

blocks

190 and 192.

At block 194, the SOC is determined₁The sum of the stored values being SOC₂Whether there is sufficient SOC swing between the stored values. Sufficient SOC swing may be described as SOC_MINAnd SOC is_MINMay represent a threshold percentage difference between the two stored SOC values. For example, SOC_MINIt may be a 5% swing, a 10% swing, a 15% swing, or another percentage swing that establishes a sufficient difference between the two SOC values for accurate capacity estimation of the energy storage component 14. If the wobble is not sufficient, the method 160 may return to the counter update at block 164.

If the SOC swings sufficiently, the control module 32 may determine whether the total current integration time is less than the maximum allowable time at block 196. For example, if the total current integration time is greater than the maximum allowed time, the current offset error may affect the capacity estimation in an undesirable manner. Therefore, it may be desirable to limit the total current integration time to less than about 50 hours. If the maximum allowed time has been exceeded, the method 160 may return to the counter update of block 164.

Alternatively, if the maximum allowable time has not been exceeded, the estimated battery capacity Q of energy storage component 14 may be calculated at block 198. To calculate the estimated battery capacity Q, the following equation may be used:

where the values used for the calculations are obtained from the values stored in

blocks

190 and 192. Subsequently, at block 200, the estimated battery capacity Q is stored in the memory 36. Further, once the estimated battery capacity Q is stored, the method 160 may return to the counter update of block 164, and the method 160 may operate recursively until an indication is provided to the control module 32 to stop the method 160.

The two

capacity estimation methods

120 and 160 described above complement each other in practice. The method 120 may not use SOC swings between two OCV relaxation events, and may use real-time SOC swings while the vehicle 10 is running. Thus, due to the design principles of the advanced start-stop and hybrid electric vehicle, the method 120 may be particularly applicable to advanced start-stop and hybrid electric vehicles to maximize the charge rate of harvested energy when there is an excess supply of kinetic energy and to maximize the discharge rate when there is a peak power consumption demand to improve fuel economy. Thus, the energy storage component 14 may establish a standby (sleep) mode at approximately 50% SOC. Therefore, the energy storage component 14 typically has a small interval between the two OCV measurements. Alternatively, due to the simplicity, accuracy, and low implementation cost of the method 160, the method 160 may be applied to enhance the robustness and accuracy of the capacity estimation of the energy storage component 14 when the vehicle 10 experiences several sleep periods during typical operation.

It may be beneficial to occasionally verify the capacity estimation of the energy storage component 14. Thus, fig. 10 is a flow chart 210 describing a verification process of the estimated battery capacity Q of the energy storage component 14. At block 212, the control module 32 determines whether the capacity estimate of the energy storage component 14 is valid. For example, if there have not been any valid capacity estimates from

methods

120 and 160 for a longer amount of time (e.g., more than two months since the last valid capacity estimate), the capacity estimate may be invalid if the most recently calculated capacity estimate exceeds a change threshold (e.g., the most recently calculated capacity estimate is 5% greater, 10% greater, 15% greater, or more greater than the previously calculated capacity estimate, or if the accuracy of the valid capacity estimate is not within an acceptable range.

In determining whether the accuracy of the effective capacity estimate is not within an acceptable range, the error of the SOC/OCV measurement may be used along with calculating the error of the capacity estimate via current integration that represents the current measurement accuracy. For example, the kalman filtering method may include an error estimate or a maximum accuracy estimate (e.g., about 3%), and evaluation of a convergence criterion as described herein may refine such an error estimate. After refining the error estimate, a time or energy throughput related error increase based on expected aging under observed conditions of the battery system 12 may be applied to the error estimate. Thus, if the capacity estimate is determined within a certain accuracy, the error steadily increases until there is a chance to reach the new estimate with a lower error, which will reset the error estimate.

If the capacity estimate is determined to be valid, the current capacity estimate may be updated at block 214. The updated capacity at block 214 may be used at block 216 as the actual capacity of the energy storage assembly 14 during the current integration process that uses the current capacity estimate (e.g., using equation 35 above). The result of the current integration process using the actual capacity of the energy storage component is the value of SOC (1) over an integration period calculated at block 218.

Alternatively, if the capacity estimate is determined to be invalid (e.g., the average error is too high and the reset does not improve accuracy), then the candidate capacity may be used in a current integration process that is parallel to the current integration process of block 216 at block 220. The candidate capacity may be 5% less than the actual capacity used in the current integration process of block 216. The result of the current integration process using the candidate capacity is the value of SOC (2) over an integration period calculated at block 222. In addition, the measured parameter 224 of the energy storage component 14 may be used when performing the current integration process at

blocks

216 and 220. The measured parameters 224 may include system/sensor specifications, temperature, current, and voltage of the energy storage component 14.

To effectively use the verification process of flowchart 210, an accurate initial SOC at the beginning of the parallel current integration process may be used. Thus, the measured parameter 224 may provide a value for the battery control module 32 to calculate an accurate initial SOC. For example, if the vehicle 10 exits the longer sleep period of the energy storage component 14 prior to the parallel current integration process at

blocks

216 and 220, the open circuit voltage 44 of the energy storage component 14 may be measured from the measured parameter 224, as discussed in detail above. Using the open circuit voltage 44, the open circuit voltage to state of charge lookup table stored in memory 36 may be consulted by the control module 32 to calculate an accurate initial SOC value. It can also be appreciated that a significant SOC delta (e.g., SOC swing) between the initial SOC at the beginning of the parallel current integration process and the final SOC at the point in time at which the changed capacity estimate is evaluated may be beneficial to accurately evaluating the effectiveness of the capacity estimate. The value may be represented by Δ SOC^δQAnd (4) showing.

Additionally, a kalman filter may be used at block 226 at the point in time when the change capacity estimate is evaluated for comparison to the SOC value produced by the parallel current integration process. For example, using the method 70 discussed above in connection with fig. 6A and 6B, an estimated SOC value (SOC (3)) for the energy storage component 14 may be calculated by the control module 32 at block 228. Alternatively or additionally, if the energy storage component 14 is in a resting state, the OCV44 may be obtained from the energy storage component 14 at block 230. At block 232, the lookup of the OCV to SOC lookup table by the control module 32 results in the calculation of SOC (4) at block 234.

After calculating SOC (1) -SOC (3) and/or SOC (4), a directional comparison of SOC values may be performed by the control module 32 at block 236. For example, the values of SOC (3) and SOC (4) at the time point at which the change capacity estimation value is evaluated may be compared with the values of SOC (1) and SOC (2) at the same time point. This comparison may provide many details regarding the new capacity estimate for the energy storage component 14. The control module 32 may consider the estimated capacity value calculated from SOC (3) and/or SOC (3) as valid if the value of SOC (3) and/or SOC (4) falls within the range of the values of SOC (1) and SOC (2) or the value of SOC (3) and/or SOC (4) is in the same direction as the value of SOC (2) with respect to SOC (1). In this case, the control module 32 may calculate the capacity at this point in time and update the actual capacity value to the newly calculated estimated capacity at block 214.

Alternatively, if the values of SOC (3) and/or SOC (4) do not fall within the range of the values of SOC (1) and SOC (2), the control module 32 may consider the estimated capacity values from SOC (3) and/or SOC (4) to be invalid at block 236. In this case, the process of flow chart 210 may be resumed at a different initial SOC value, or SOC (3) and/or SOC (4) may be calculated at a later time to determine whether the capacity value based on SOC (3) and/or SOC (4) is valid.

Turning to fig. 11, a diagram 240 illustrates the process detailed in the flow chart 210 of fig. 10. An ordinate 242 represents the SOC of the energy storage component 14 in percent. The abscissa 244 represents the time the SOC is measured. Line 246 represents the current integral of the energy storage component 14 using the actual capacity of the energy storage component, and line 248 represents the parallel current integral of the energy storage component 14 using the candidate capacity of the energy storage component 14, which as shown is 5% lower than the actual capacity of the energy storage component 14.

As shown, the parallel current integration process is at time t₁Starting with an accurate initial SOC value 250. An accurate initial SOC value 250 may be obtained by an Open Circuit Voltage (OCV) measurement and a comparison of the OCV measurement to an OCV to SOC lookup table. In addition, a parallel current integration process may be performed until time t₂. Time t₂Δ SOC which can represent a parallel current integration process^Q(e.g., state of charge swing) is a time sufficient to accurately verify the estimated capacity of the energy storage component 14.For example, the state of charge swing may be a swing of about 20% in order to accurately verify the estimated capacity. In other cases, the state of charge swing may be a swing of about 10%, 15%, or up to 25% or more for accurate verification of estimated capacity.

Approaching time t as the parallel integration process approaches₂

Several SOC measurements

252 and 254 of the energy storage component, for example calculated using a kalman filtering method, are plotted. Dark SOC measurement 252 represents an SOC measurement that is not valid for a capacity estimation update. For example, the SOC swing (e.g., Δ SOC) with the parallel current integration lines 246 and 248^δQ) In contrast, the change in SOC between line 246 and SOC measurement 252 (e.g., Δ SOC)^k) In the opposite direction. Thus, if the value of dark SOC measurement 252 is calculated by control module 32, control module 32 will wait for a subsequent valid SOC measurement to update the capacity estimation value.

Alternatively, light colored SOC measurement 254 represents an SOC measurement that is valid for a capacity estimation update. For example, the change in SOC between line 246 and SOC measurement 254 (e.g., Δ SOC)^k) SOC swings (e.g., Δ SOC) with parallel current integration lines 246 and 248^δQ) The directions are the same. Thus, if the value of light color SOC measurement 254 is calculated by control module 32, control module 32 will update the capacity estimation value when light color SOC measurement 254 is calculated.

One or more of the disclosed embodiments may provide, alone or in combination, one or more technical effects, including determining a time-varying variable and a time-invariant variable of a battery, determining a state of charge of the battery, determining a state of health of the battery, and verifying the state of health of the battery. The technical effects and technical problems in the specification are exemplary and not restrictive. It should be noted that the embodiments described in the specification may have other technical effects and may solve other technical problems.

Although only certain features and embodiments have been illustrated and described, many modifications and changes may occur to those skilled in the art (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperatures, pressures, etc.), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the disclosed subject matter. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the disclosure. Moreover, in an effort to provide a concise description of the exemplary embodiments, all features of an actual implementation may not be described. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure, without undue experimentation.

Claims

1. A battery system, comprising:

a battery configured to be coupled to an electrical system;

one or more sensors configured to measure battery parameters during operation of the battery; and

a control module communicatively coupled to the one or more sensors, wherein the control module is configured to:

determining a first Kalman filter based at least in part on an equivalent circuit model of the battery describing a relationship between the battery parameters and model parameters, wherein:

the model parameters include an open circuit voltage of the battery, a current path resistance of the battery, and a charge transfer resistance of the battery; and

the first Kalman configuration is configured to implement the open circuit voltage of the battery as a time-varying parameter, the current path resistance of the battery as a first time-invariant parameter, and the charge transfer resistance of the battery as a second time-invariant parameter;

executing the first Kalman filter based on a first set of a plurality of battery parameter sets to determine first estimated model parameters, wherein the first estimated model parameters comprise one of a first estimated open circuit voltage of the battery, a first estimated current path resistance of the battery, and a first estimated charge transfer resistance of the battery;

determining a first model parameter based at least in part on convergence of a plurality of estimated model parameters, each estimated model parameter determined based on a different set of the plurality of battery parameter sets; and

controlling charging, discharging, or both of the battery based at least in part on the first model parameters.

2. The battery system of claim 1, wherein:

the control module is configured to execute the first Kalman filter based on a second set of the plurality of battery parameter sets to determine second estimation model parameters; and

the second estimated model parameter comprises a second estimated open circuit voltage of the battery when the first estimated model parameter comprises the first estimated open circuit voltage, the second estimated model parameter comprises a second estimated current path resistance of the battery when the first estimated model parameter comprises the first estimated current path resistance, and the second estimated model parameter comprises a second estimated charge transfer resistance of the battery when the first estimated model parameter comprises the first estimated charge transfer resistance.

3. The battery system of claim 1, wherein the control module is configured to:

executing the first Kalman filter based on the first set of the plurality of battery parameter sets to determine second estimated model parameters, wherein the second estimated model parameters comprise the first estimated current path resistance of the battery, and the first estimated model parameters comprise the first estimated charge transfer resistance of the battery; and

determining second model parameters based at least in part on convergence of the plurality of estimated model parameters, wherein the second model parameters include the current path resistance of the battery, and the first model parameters include the charge transfer resistance of the battery.

4. The battery system of claim 3, wherein the control module is configured to test convergence of the plurality of estimated model parameters by:

determining an estimated current path resistance mean and an estimated current path resistance variance based at least in part on the first estimated current path resistance and one or more previously determined estimated current path resistances of the battery;

determining a first ratio of the estimated current path resistance variance to a square of the estimated current path resistance average;

determining an estimated charge transfer resistance mean and an estimated charge transfer resistance variance based at least in part on the first estimated charge transfer resistance and one or more previously determined estimated charge transfer resistances of the battery;

determining a second ratio of the estimated variance of charge transfer resistance to the square of the average of the estimated charge transfer resistance; and

comparing the greater of the first ratio and the second ratio to a square of a relative error tolerance value.

5. The battery system of claim 4, wherein:

the one or more sensors are configured to measure a temperature of the battery during operation; and

the control module is configured to:

determining the second model parameter by setting the first estimated current path resistance to the current path resistance of the battery when the greater of the first ratio and the second ratio is less than the square of the relative error tolerance value;

determining the first model parameter by setting the first estimated charge transfer resistance to the charge transfer resistance of the battery when the greater of the first ratio and the second ratio is less than the square of the relative error tolerance value; and

storing the current path resistance of the battery, the charge transfer resistance of the battery, and the temperature of the battery in order to monitor ohmic growth of the battery.

6. The battery system of claim 1, wherein the first kalman filter comprises a process noise matrix configured to:

implementing the open circuit voltage of the battery as the time-varying parameter;

implementing the current path resistance of the battery as the first time-invariant parameter; and

implementing the charge transfer resistance of the battery as the second time-invariant parameter.

7. The battery system of claim 6, wherein the process noise matrix includes a main diagonal having only one non-zero value.

8. The battery system of claim 1, wherein the control module is configured to:

determining a first estimated state of charge of the battery based on the first estimated model parameters when the first estimated model parameters include the first estimated open circuit voltage of the battery.

9. The battery system of claim 8, wherein the control module is configured to:

determining a second Kalman filter based at least in part on a relationship between a capacity of the battery, a state of charge change of the battery, and a charge throughput of the battery during the state of charge change;

performing the second Kalman filter to determine an estimated capacity of the battery based on the first set of the plurality of battery parameter sets and the first estimated state of charge of the battery;

determining the capacity of the battery based at least in part on convergence of a plurality of estimated battery capacities, each of the estimated battery capacities determined based on a different set of the plurality of battery parameter sets.

10. The battery system of claim 1, wherein:

the battery comprises a rechargeable battery; and

the control module includes a battery control unit configured to:

receiving the battery parameters measured by the one or more sensors coupled to the rechargeable battery;

determining the first Kalman filter based at least in part on the equivalent circuit model of the rechargeable battery describing a relationship between the battery parameters and the model parameters;

executing the first Kalman filter based on the first set of the plurality of battery parameter sets to determine the first estimation model parameters;

determining the first model parameter based at least in part on convergence of the plurality of estimated model parameters; and

controlling charging, discharging, or both of the rechargeable battery based at least in part on the first model parameters in order to improve a life of the rechargeable battery, a fuel efficiency of a motor vehicle, or both.

11. The battery system of claim 1, wherein the battery comprises:

a housing;

a first terminal and a second terminal coupled to the housing;

a first battery cell using a first battery chemistry, wherein the first battery cell is disposed within the housing and electrically coupled to the first terminal and the second terminal;

a second battery cell using a second battery chemistry different from the first battery chemistry used by the first battery cell, wherein the second battery cell is disposed within the housing and electrically coupled to the first terminal and the second terminal; and

a battery control unit disposed within the housing, wherein:

the control module comprises the battery control unit and a vehicle control unit; and is

The battery control module is configured to:

receiving the battery parameters measured by the one or more sensors;

determining the first Kalman filter based at least in part on the equivalent circuit model of the battery describing a relationship between the battery parameters and the model parameters;

determining the first model parameter based at least in part on convergence of the plurality of estimated model parameters, each estimated model parameter determined based on a different set of the plurality of battery parameter sets; and

the vehicle control unit is configured to control operation of the electrical system to control charging, discharging, or both of the battery based at least in part on the first model parameter in order to improve a life of the battery, a fuel efficiency of a motor vehicle, or both.

12. A method for operating a battery control module, comprising:

receiving, using a battery control module, battery parameters measured by one or more sensors coupled to a rechargeable battery;

determining a first Kalman filter using the battery control module based at least in part on an equivalent circuit model of the rechargeable battery describing a relationship between the battery parameters and model parameters, wherein the model parameters include an open circuit voltage of the rechargeable battery, a current path resistance of the rechargeable battery, and a charge transfer resistance of the rechargeable battery;

determining first estimated model parameters using the battery control module to execute the first Kalman filter based on a first set of a plurality of battery parameter sets, wherein the first estimated model parameters comprise one of a first estimated open circuit voltage of the rechargeable battery, a first estimated current path resistance of the rechargeable battery, and a first estimated charge transfer resistance of the rechargeable battery;

determining, using the battery control module, a first model parameter based at least in part on convergence of a plurality of estimated model parameters, each of the plurality of estimated model parameters determined based on a different set of the plurality of battery parameter sets; and

controlling, using the battery control module, charging, discharging, or both of the rechargeable battery based at least in part on the first model parameters.

13. The method of claim 12, the method comprising:

determining, using the battery control module, a first estimated state of charge of the rechargeable battery based on the first estimated model parameter when the first estimated model parameter comprises the first estimated open circuit voltage of the rechargeable battery;

and/or wherein the method further comprises the steps of:

determining, using the battery control module, a second Kalman filter based at least in part on a relationship between a capacity of the rechargeable battery, a state of charge change of the rechargeable battery, and a charge throughput of the rechargeable battery during the state of charge change;

determining an estimated capacity of the rechargeable battery using the battery control module to execute the second Kalman filter based on the first set of the plurality of battery parameter sets and the first estimated state of charge of the rechargeable battery; and

determining the capacity of the rechargeable battery using the battery control module based at least in part on convergence of a plurality of estimated battery capacities, each of the plurality of estimated battery capacities determined based on a different set of the plurality of battery parameter sets.

14. A motor vehicle comprising:

a battery, wherein the battery comprises a plurality of battery cells;

an electrical system comprising an alternator configured to generate electrical energy in operation, and an electrical load configured to operate using the electrical energy;

a relay electrically coupled between the plurality of battery cells and the electrical system;

one or more sensors configured to measure a plurality of battery parameter sets during operation of the battery, wherein each battery parameter set of the plurality of battery parameter sets comprises a terminal voltage and a terminal current; and

one or more control modules communicatively coupled to the relay and the one or more sensors, wherein the one or more control modules are configured to:

determining a battery model describing a relationship between the terminal voltage and the terminal current of the battery, the battery model having an open circuit voltage of the battery, an ohmic resistance of the battery, and a charge transfer resistance of the battery;

determining a Kalman filter based at least in part on the relationship described by the battery model;

determining a plurality of ohmic resistances and a plurality of charge transfer resistances by executing the Kalman filter based at least in part on each battery parameter set of the plurality of battery parameter sets;

determining a state of health of the battery based at least in part on the plurality of ohmic resistances and the plurality of charge transfer resistances.

15. The motor vehicle according to claim 14, wherein the plurality of battery cells include:

a first battery cell using a first battery chemistry; and

a second battery cell using a second battery chemistry.

16. The motor vehicle of claim 14, wherein the one or more control modules are configured to:

determining an average ohmic resistance of the plurality of ohmic resistances;

determining an ohmic resistance variance of the plurality of ohmic resistances;

determining a first ratio of the ohmic resistance variance to a square of the average ohmic resistance;

determining an average charge transfer resistance of the plurality of charge transfer resistances;

determining a charge transfer resistance variance of the plurality of charge transfer resistances;

determining a second ratio of the variance of the charge transfer resistance to the square of the average charge transfer resistance; and

determining whether a greater of the first ratio and the second ratio is greater than a relative error tolerance threshold.

17. A motor vehicle in accordance with claim 16, wherein:

each battery parameter set of the plurality of battery parameter sets includes a battery temperature; and

one or more control modules are configured to determine the state of health of the battery based at least in part on the average ohmic resistance, the average charge transfer resistance, and the battery temperature included in one or more of the plurality of battery parameter sets.

18. The motor vehicle of claim 14, wherein the one or more control modules are configured to determine the state of health of the battery from an ohmic resistance increase perspective.

19. The motor vehicle of claim 14, the one or more control modules configured to:

determining the open circuit voltage of the battery by executing the Kalman filter based at least in part on a set of battery parameters of the plurality of battery parameter sets;

determining a state of charge of the battery based at least in part on the open circuit voltage of the battery.

20. The motor vehicle of claim 14, wherein the one or more control modules are configured to initialize parameters of the kalman filter with random values prior to executing the kalman filter based at least in part on the plurality of battery parameter sets.

21. A motor vehicle in accordance with claim 14, wherein:

the one or more control modules are communicatively coupled to the alternator; and

the one or more control modules are configured to control charging of the battery by controlling the electrical energy output by the alternator.

22. The motor vehicle of claim 21, wherein the one or more control modules are configured to control switching of the relay and control electrical energy output by the alternator.

23. A motor vehicle in accordance with claim 14, wherein:

the open circuit voltage of the battery comprises a time-varying parameter, the ohmic resistance of the battery comprises a first time-invariant parameter, the charge transfer resistance of the battery comprises a second time-invariant parameter; or

The open circuit voltage of the battery comprises a fast time varying parameter, the ohmic resistance of the battery comprises a first slow time varying parameter, and the charge transfer resistance of the battery comprises a second slow time varying parameter.

24. A method, the method comprising:

receiving, using one or more processors applied to a vehicle, a first set of battery parameters comprising a first terminal voltage and a first terminal current measured by one or more sensors during battery operation applied to the vehicle;

determining, using the one or more processors, a battery model describing a first relationship between a terminal voltage of the battery, a terminal current of the battery, an open circuit voltage of the battery, an ohmic resistance of the battery, and a charge transfer resistance of the battery;

determining, using the one or more processors, a Kalman filter based at least in part on the first relationship described by the battery model;

determining, using the one or more processors, a first state of charge of the battery based at least in part on executing the Kalman filter using the first battery parameter set.

25. The method of claim 24, comprising:

receiving, using the one or more processors, a second set of battery parameters comprising a second terminal voltage and a second terminal current measured by the one or more sensors during operation of the battery after the first set of battery parameters;

determining, using the one or more processors, the second state of charge of the battery based at least in part on executing the Kalman filter using the second set of battery parameters.

26. The method of claim 25, comprising:

determining, using the one or more processors, a first ohmic resistance of the battery and a first charge transfer resistance of the battery by executing the Kalman filter based at least in part on the first battery parameter set;

determining, using the one or more processors, a second ohmic resistance of the battery and a second charge transfer resistance of the battery by executing the Kalman filter based at least in part on the second set of battery parameters;

determining, using the one or more processors, a state of health of the battery based at least in part on convergence of the first and second ohmic resistances and convergence of the first and second charge transfer resistances.

27. The method of claim 25, comprising, using the one or more processors, determining a second relationship between the state of charge of the battery and the open circuit voltage of the battery, wherein:

determining the first state of charge of the battery comprises:

determining a first open circuit voltage of the battery by executing the Kalman filter based at least in part on the first battery parameter set; and

mapping the first open-circuit voltage to the first state of charge based at least in part on the second relationship between the state of charge of the battery and the open-circuit voltage of the battery; and

determining the second state of charge of the battery comprises:

determining a second open circuit voltage of the battery by executing the Kalman filter based at least in part on the second battery parameter set; and

mapping the second open circuit voltage to the second state of charge based at least in part on the second relationship between the state of charge of the battery and the open circuit voltage of the battery.